Riemannian Submersions and Related Topics

By M. Falcitelli, A. Pastore, S. Ianuş. 2004

398 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ca7870fcd8924332dd034ab9e7c1054ec1eac5e6

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In Astronomy and Astrophysics

Citations in the corpus

Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries (2011, background): “Ais the skew-symmetrization of −1 2T. The connection form θis a Yang-Mills connection if for every horizontal vector ﬁeld X, the vertical component of Xd ℓ=1 (∇X ℓ T)(Xℓ,Xk) is zero (see for instance [19], p. 146). As a consequence of Theorem 2.19, we then obtain the following result. CURVATURE-DIME”
Slant submersions from almost product Riemannian manifolds (2013, positive): “A Riemannian submersion π : M → B determines 2 (1, 2) tensor fields T and A on M, by the following formulas: T (E,F ) = TEF = h∇vEvF + v∇vEhF (2) and A(E,F ) = AEF = v∇hEhF + h∇hEvF (3) for any E,F ∈ Γ(TM), where v and h are the vertical and horizontal projections (see [7]).”
The Geometry of Filtering (2008, background): “The book [33] shows the breadth of geometric structures which can be consi dered in association with Riemannian submersions.”
Conformal anti-invariant submersions from almost Hermitian manifolds (2015, background): “Riemannian submersions between Riemannian manifolds were studied by O’Neill [18] and Gray [10]; for recent developments on the geometry of Riemannian submanifolds and Riemannian submersions, see [4] and [8], respectively.”
Anti-invariant Riemannian submersions from almost Hermitian manifolds (2010, background): “However, a very general class of solutions is given by Riemannian submersions from the extra dimensional space onto the space in which the scalar fields take values (see [6], chapter 9).”
Semi-invariant Submersions from Almost Hermitian Manifolds (2010, background): “Later such submersions have been studied widely in differential geometry; for details, see [5].”
Sub-Riemannian Curvature in Contact Geometry (2015, methodology): “This deﬁnition coincides with the classical one given in [16, Sec.”
Conformal Riemannian Maps between Riemannian Manifolds, Their Harmonicity and Decomposition Theorems (2010, methodology): “On the other hand, the study of Riemannian submersions between Riemannian manifolds was initiated by O’Neill [31] and Gray [18], see also [12] and [41].”